Question

In ABCD, the measure of ZD=90°, CB = 61, DC = 60, and BD = 11. What is the value

of the tangent of ZB to the nearest hundredth?

Answer 1

The value of the tangent of ZB, to the nearest hundredth, in ABCD is 36.76 (rounded to nearest hundredth).

Step-by-step explanation:

In a right triangle, the tangent of an angle is equal to the length of the side opposite that angle divided by the length of the side adjacent to that angle. In this case, we want to find the tangent of angle ZB.

Since ZD is a right angle, we know that angle ZCB is also a right angle. So, we can say that angle BCD is equal to angle ZBC, which is 90 degrees minus the measure of angle ZB.

Using this information, we can find the value of angle BCD:

BCD = 90 - ZB

Now, let's find the lengths of the sides DC and BD:

DC = 60

BD = 11

Next, let's find the length of CB:

CB² = DC² + BD² (Pythagorean theorem)

CB² = 60² + 11²

CB² = 3600 + 121

CB² = 4811

CB = √(4811) (taking square root)

CB = 220.55 (rounded to nearest hundredth)

Now, let's find the value of tangent of ZB:

tan(ZB) = opp(ZB) / adj(ZB) (tangent formula)

tan(ZB) = CB / DC (substituting values)

tan(ZB) = 220.55 / 60 (rounded to nearest hundredth)

tan(ZB) = 36.76 (rounded to nearest hundredth)